Details

analyze1.4s (22.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (20.2%)

Results

1.1s	8255×	body	128	valid
105.0ms	718×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify115.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1691×	`fma-neg_binary64`
841×	`div-sub_binary64`
807×	`distribute-rgt-in_binary64`
769×	`fma-def_binary64`
504×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	19	16
2	40	14
3	82	14
4	166	14
5	297	14
6	643	14
7	1551	14
8	3111	14
9	3064	14
10	3153	14
11	3152	14
12	3170	14
13	3201	14
14	5494	14

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	12.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	2.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series59.0ms (1%)

Counts

2 → 96

Calls

2 calls:

41.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
17.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite95.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

365×	`fma-def_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
193×	`log-pow_binary64`

Counts

2 → 79

Calls

2 calls:

93.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
93.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	227	24
2	3258	24
3	4982	24
4	4996	24
0	0	0
1	0	0

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-def_binary64`
656×	`times-frac_binary64`
497×	`fma-neg_binary64`
494×	`cancel-sign-sub-inv_binary64`
324×	`sub-neg_binary64`

Counts

175 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	2936
1	482	2936
2	1844	2292
3	4561	2286
4	4998	2286

prune118.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	149	5	154
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	150	6	156

Error

0.0b

Counts

156 → 6

Alt Table

Status	Error	Program
▶	2.1b	(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
✓	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	2.4b	(fma.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2)) x)
	2.2b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)
	3.4b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) 2))
	3.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))

Compiler

Compiled 3557 to 1213 computations (65.9% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.3b	(pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1)
✓	2.0b	(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)

series151.0ms (2.5%)

Counts

3 → 132

Calls

3 calls:

90.0ms	(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
45.0ms	(pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1)
17.0ms	(/.f64 (-.f64 z a) (-.f64 z t))

rewrite70.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

369×	`fma-def_binary64`
251×	`expm1-udef_binary64`
251×	`log1p-udef_binary64`
205×	`fma-neg_binary64`
141×	`add-sqr-sqrt_binary64`

Counts

3 → 124

Calls

3 calls:

67.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
67.0ms	(pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1)
67.0ms	(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	269	34
2	3641	34
3	4940	34
0	0	0
1	0	0

simplify118.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/l*_binary64`
490×	`associate-/r*_binary64`
308×	`associate--l+_binary64`
261×	`associate-r_binary64`
192×	`+-commutative_binary64`

Counts

256 → 256

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	514	7109
1	1673	6956
2	5109	6956

prune246.0ms (4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	256	6	262

Error

0.0b

Counts

262 → 6

Alt Table

Status	Error	Program
✓	2.1b	(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
✓	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	2.4b	(fma.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2)) x)
	3.4b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) 2))
▶	2.1b	(fma.f64 y (/.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (-.f64 z t))) x)
	3.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))

Compiler

Compiled 9047 to 3760 computations (58.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z t))
✓	0.0b	(/.f64 1 (-.f64 z a))
✓	0.2b	(/.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (-.f64 z t)))
✓	2.0b	(fma.f64 y (/.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (-.f64 z t))) x)

series73.0ms (1.2%)

Counts

4 → 144

Calls

4 calls:

37.0ms	(fma.f64 y (/.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (-.f64 z t))) x)
17.0ms	(/.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (-.f64 z t)))
10.0ms	(/.f64 1 (-.f64 z t))
8.0ms	(/.f64 1 (-.f64 z a))

rewrite76.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

819×	`prod-diff_binary64`
150×	`add-sqr-sqrt_binary64`
142×	`log1p-expm1-u_binary64`
142×	`expm1-log1p-u_binary64`
138×	`add-cbrt-cube_binary64`

Counts

4 → 115

Calls

4 calls:

73.0ms	(/.f64 1 (-.f64 z t))
73.0ms	(/.f64 1 (-.f64 z a))
73.0ms	(/.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (-.f64 z t)))
73.0ms	(fma.f64 y (/.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (-.f64 z t))) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	291	38
2	3810	38
3	5437	38
0	0	0
1	0	0

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
773×	`times-frac_binary64`
505×	`cancel-sign-sub-inv_binary64`
342×	`sub-neg_binary64`
186×	`+-commutative_binary64`

Counts

259 → 217

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	3920
1	600	3890
2	2238	3582
3	5107	3582

prune158.0ms (2.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	217	6	223

Error

0.0b

Counts

223 → 6

Alt Table

Status	Error	Program
✓	2.1b	(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
✓	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
▶	2.4b	(fma.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2)) x)
	3.4b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) 2))
✓	2.1b	(fma.f64 y (/.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (-.f64 z t))) x)
	3.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))

Compiler

Compiled 4903 to 1970 computations (59.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2))
✓	0.3b	(pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2)
✓	2.0b	(fma.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2)) x)
✓	5.0b	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))

series277.0ms (4.5%)

Counts

4 → 168

Calls

4 calls:

135.0ms	(pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2)
84.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))
40.0ms	(fma.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2)) x)
18.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2))

rewrite82.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

384×	`fma-def_binary64`
262×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
210×	`fma-neg_binary64`
148×	`add-sqr-sqrt_binary64`

Counts

4 → 132

Calls

4 calls:

79.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2))
79.0ms	(pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2)
79.0ms	(fma.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2)) x)
79.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	51
1	291	51
2	3784	51
3	5117	51
0	0	0
1	0	0

simplify188.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-def_binary64`
365×	`*-commutative_binary64`
252×	`+-commutative_binary64`
227×	`sub-neg_binary64`
175×	`associate-+r+_binary64`

Counts

300 → 329

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1025	12393
1	3648	12187
2	5218	12187

prune576.0ms (9.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	423	0	423
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	423	6	429

Error

0.0b

Counts

429 → 6

Alt Table

Status	Error	Program
✓	2.1b	(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
✓	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	2.4b	(fma.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2)) x)
	3.4b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) 2))
✓	2.1b	(fma.f64 y (/.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (-.f64 z t))) x)
	3.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))

Compiler

Compiled 26358 to 13351 computations (49.3% saved)

regimes790.0ms (12.8%)

Accuracy

Total 0.7b remaining (97.2%)

Threshold costs 0.7b (97.2%)

Counts

73 → 3

Compiler

Compiled 9123 to 5553 computations (39.1% saved)

bsearch26.0ms (0.4%)

Steps

Iters	Range		Point
3	1.4971378104384128e-238	8.175234475707689e-230	2.8892448090824406e-235
5	-1.6152471411622293e-96	-2.384808946983277e-98	-1.74052409511644e-97

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	71
1	39	71
2	51	71
3	64	71
4	71	71
5	74	71
6	75	71
7	74	71

end102.0ms (1.7%)

Compiler: Compiled 232 to 123 computations (47% saved)

Details

analyze1.4s (22.1%)

sample1.2s (20.2%)

simplify115.0ms (1.9%)

prune6.0ms (0.1%)

localize7.0ms (0.1%)

series59.0ms (1%)

rewrite95.0ms (1.5%)

simplify91.0ms (1.5%)

prune118.0ms (1.9%)

localize10.0ms (0.2%)

series151.0ms (2.5%)

rewrite70.0ms (1.1%)

simplify118.0ms (1.9%)

prune246.0ms (4%)

localize9.0ms (0.2%)

series73.0ms (1.2%)

rewrite76.0ms (1.2%)

simplify86.0ms (1.4%)

prune158.0ms (2.6%)

localize13.0ms (0.2%)

series277.0ms (4.5%)

rewrite82.0ms (1.3%)

simplify188.0ms (3.1%)

prune576.0ms (9.4%)

regimes790.0ms (12.8%)

bsearch26.0ms (0.4%)

simplify6.0ms (0.1%)

end102.0ms (1.7%)

Profiling